The Dilogarithm Function in Geometry and Number Theory (Pt. 1)

Abstract: 

In this first part of a series of talk, we introduce and explore basic properties of the famous dilogarithm. First defined by Euler, the dilogarithm function is one of the simplest non-elementary functions, but also one of the strangest. It was also studied by mathematicians such as Abel, Lobachevsky, Kummer, and Ramanujan among others. In recent years, it has become much better known due to its connections with hyperbolic geometry, algebraic K-theory and mathematical physics. We explore some of these connections and present some applications in geometry and number theory.